Fig. shows two blocks of masses 5kg and 2kg placed on a frictionless surface and connected by a spring. An external kick gives a velocity 14 m/ s to the heavier block in the direction of lighter one. Deduce (i) the velocity gained by the centre of mass and (ii) the separate velocities of the two blocks in the centre of mass coordinates just after the kick.
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- The velocity of centre of mass $v_{cm}$ is given by the expression
Here $m_1 = 5kg, m_2 = 2kg, v_1 = 14m/s v_2 = 0$
Substituting these values, we get
$\text{v}_{\text{cm}}=\frac{5\times14+2\times0}{5+2}10\text{m/s}$
- We know that the centre of mass coordinate reference frame is one in which centre of mass is at rest. So the velocity of heavier block in this frame just after the kick is
and that of lighter block is
$\text{v}_2'=\text{v}_1-\text{v}_{\text{cm}}=0-14=-10\text{m/s}.$
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